In wireless communications, information is typically communicated in symbols that are encoded onto a radio frequency (RF) signal by a modulation scheme that receiver devices can detect and decode to recover the data symbols from received RF signals. In a conventional single carrier system, the transmitted signals containing the information or data to be sent are usually represented as complex modulation symbols using phase shift keying (PSK) or quadrature amplitude modulation (QAM). Vestigial sideband modulation (VSB) is another modulation method which attempts to eliminate the spectral redundancy of pulse amplitude modulated (PAM) signals. Modulating a real data sequence by a cosine carrier results in a symmetric double-sided pass band spectrum. The symmetry implies that one of the sidebands is redundant, and removing one sideband with an ideal brick wall filter should preserve the ability for perfect demodulation.
In both cases, the signals are modulated on a carrier for transmission over a communication channel before they are received by a receiver at the other end of the channel. The main objective of data reception is to recover the transmitted data as perfectly as possible. Recovery of the encoded information is often limited by the amount of distortion and noise introduced in the received signal resulting from a variety of sources and phenomenon within the transmission path, which is referred to generally as the “channel.” Thus, improvements in signal reception may be accomplished by reducing or eliminating the distortions and improving the filtering of the transmitted signal from the noise in the communication channel.